I am regularly sweeping and wet mopping my 400 sf garage studio. I am aware that a lot of clay dust gets airborne. Can anyone recommend a good shop vac with HEPA filter to use instead of sweeping?

wet mopping is the best way to clean the studio in terms of health.... A really good HEPA vac would likely work, you're looking at around 500.00 for the vac itself, and sometimes as much as 300.00 for replacement filters... Also I would suspect that with the quantity of dust you will be moving through the vac you'll go through filters like nobody's business... Any non hepa vac (like those irobots) will just throw dust back into the air--bad bad bad. wet mop, rinse, lather, repeat.

The way I think is best to vacuum, is to have the vacuum unit outside, for my shop and studio I us a shop vac with a 50 foot hose and commercial style wand. I put the vacuum outside or just in the doorway with the exhaust pointing out, no issues with dust at all, except when emptying the vacuum, I wear a good respirator, and empty the vac outside.
For about $200. you can have the complete system, attached is a picture of my system, a link to WalVac, which is where I got my hose and wand and a link to ebay to show some hose availability, I did have to make an adapter for the hose to the vacuum, also pictured.
For a 50' hose it should be a 1-1/2" ID hose, and commercial wand, for a 30' hose, 1-1/4" ID and household wand will work. The paper filter that my vacuum came with works quite well, and has lasted a long time.
The more powerful the vacuum the better for these long hoses.

Placing the unit outside the studio makes all the sense in the world. We have a central vac system for the house and the noise and dust is outside as well.I just may have to make one for the shop.
Mark

Another vote for Nilfisk vacuum products. Have 2 in our studio, one large GS82 and a smaller unit that I don't know the model - I cannot imagine not having one. Another great thing to have in studio for cleaning is a squeegee vacuum. I use a Typhoon EV and what's great about it is you just wet the floor and suck it up! Cleans much better than a mop.